Small hexacronic icositetrahedron
# Small hexacronic icositetrahedron

Small hexacronic icositetrahedron :

| Type | Star polyhedron |
| - | - |
| Face | |
| Elements | F = 24, E = 48 V = 20 (χ = −4) |
| Symmetry group | $O_h,$ [4,3], *432 |
| Index references | $DU_{13}$ |
| dual polyhedron | Small cubicuboctahedron |

In geometry, the small hexacronic icositetrahedron is the dual of the small cubicuboctahedron. It is visually identical to the small rhombihexacron. A part of each dart lies inside the solid, hence is invisible in solid models.

## Proportions

Its faces are darts, having two angles of $\arccos({\frac {1}{4}}+{\frac {1}{2}}{\sqrt {2}})\approx 16.842\,116\,236\,30^{\circ }$, one of $\arccos({\frac {1}{2}}-{\frac {1}{4}}{\sqrt {2}})\approx 81.578\,941\,881\,85^{\circ }$ and one of $360^{\circ }-\arccos(-{\frac {1}{4}}-{\frac {1}{8}}{\sqrt {2}})\approx 244.736\,825\,645\,55^{\circ }$. Its dihedral angles equal $\arccos({\frac {-7-4{\sqrt {2}}}{17}})\approx 138.117\,959\,055\,51^{\circ }$. The ratio between the lengths of the long edges and the short ones equals $2-{\frac {1}{2}}{\sqrt {2}}\approx 1.292\,893\,218\,81$.

